Mauchly's test test for whether a covariance matrix can be assumed to
be proportional to a given matrix.
This is a generic function with methods for classes "mlm" and
"SSD".
The basic method is for objects of
class SSD the method for mlm objects just extracts the
SSD matrix and invokes the corresponding method with the same options
and arguments.
The T argument is used to transform the observations prior to
testing. This typically involves transformation to intra-block
differences, but more complicated within-block designs can be
encountered, making more elaborate transformations necessary. A
matrix T can be given directly or specified as
the difference between two projections onto the spaces spanned by
M and X, which in turn can be given as matrices or as
model formulas with respect to idata (the tests will be
invariant to parametrization of the quotient space M/X).
The common use of this test is in repeated measurements designs, with
X = ~1. This is almost, but not quite the same as testing for
compound symmetry in the untransformed covariance matrix.
Notice that the defaults involve p, which is calculated
internally as the dimension of the SSD matrix, and a couple of hidden
functions in the stats namespace, namely proj which
calculates projection matrices from design matrices or model formulas
and Thin.row which removes linearly dependent rows from a
matrix until it has full row rank.